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LGBT, or GLBT, is an initialism that stands for lesbiangaybisexual, and transgender. In use since the 1990s, the term is an adaptation of the initialism LGB, which was used to replace the term gay in reference to the LGBT community beginning in the mid-to-late 1980s.[1] Activists believed that the term gay community did not accurately represent all those to whom it referred.

Despite the fact that LGBT does not nominally encompass all individuals in smaller communities (see Variants below), the term is generally accepted to include those not specifically identified in the four-letter initialism.






The main image of this album is a mid shot of the artist witch appears to be behind a glass that has a bullet hole thought the middle. The artist is wearing a diamond cross witch signifies that he is religious. The artist is also wearing designer clothes, this combined with the diamond cross suggest that he is rich and that he has succeeded the message of this album "get rich or die tryin" 



The fire triangles or combustion triangles or ″fire diamond″ are simple models for understanding the necessary ingredients for most fires.[1]

The triangle illustrates the three elements a fire needs to ignite: heatfuel, and an oxidizing agent (usually oxygen). A fire naturally occurs when the elements are present and combined in the right mixture,[2] meaning that fire is actually an event rather than a thing. A fire can be prevented or extinguished by removing any one of the elements in the fire triangle. For example, covering a fire with a fire blanketremoves the oxygen part of the triangle and can extinguish a fire. In large fires where firefighters are called in, decreasing the amount of oxygen is not usually an option because there is no effective way to make that happen in an extended area.

The fire tetrahedron represents the addition of a component in the chemical chain reaction, to the three already present in the fire triangle. Once a fire has started, the resulting exothermic chain reaction sustains the fire and allows it to continue until or unless at least one of the elements of the fire is blocked. Foam can be used to deny the fire the oxygen it needs. Water can be used to lower the temperature of the fuel below the ignition point or to remove or disperse the fuel. Halon can be used to remove free radicals and create a barrier of inert gas in a direct attack on the chemical reaction responsible for the fire.[4]

Combustion is the chemical reaction that feeds a fire more heat and allows it to continue. When the fire involves burning metals like lithiummagnesiumtitanium,[5]etc. (known as a class-D fire), it becomes even more important to consider the energy release. The metals react faster with water than with oxygen and thereby more energy is released. Putting water on such a fire results in the fire getting hotter or even exploding. Carbon dioxide extinguishers are ineffective against certain metals such as titanium.[5] Therefore, inert agents (e.g. dry sand) must be used to break the chain reaction of metallic combustion.

In the same way, as soon as one of the four elements of the tetrahedron is removed, combustion stops.



The painting Vertumnus(ca. 1590) by Giuseppe Arcimboldo depicts Rudolf II as Vertumnus.



In Adventures of the Galaxy Rangers, The Series 5 Rangers are also a quaternity. The series actually has very few episodes where all four are heavily involved, mostly breaking the team up into groups of two or three.



ST. PAUL (KMSP) - During the renovation at the State Capitol, some of the paintings currently hanging on the walls may be replaced. The reason is some of the paintings have been deemed offensive and historically inaccurate.


Treuer who specializes in the Ojibwe language and American Indian studies says some of the pieces portraying Native Americans are insensitive or inaccurate.



“For example there's one of father Hennepin discovering St. Anthony Falls holding up a cross. Half naked Indian women running around. At the time, father Hennepin was actually a captive of the Dakota Indians,” Treuer said.




The Qabalah is usually classed under four heads:


(α) The practical Qabalah.


(β) The literal Qabalah.


(γ) The unwritten Qabalah.


(δ) The dogmatic Qabalah.



A significant step towards that vocabulary’s refinement can be found in a massive oil painting not in the exhibition, The Bather (1983)—a reinvention of Matisse’s Bathers by the River (1913)—and more intimately in two smaller watercolors executed in the same year which are on display: Mexico Chinapa and Mexico 12.23.83. In Matisse’s mural-sized oil, four statuesque nudes, chiselled with sharp Cubist edges, stretch like marble columns, canvasheight, against an insinuation of river bank. Also undertaken after a visit to Morocco, Matisse’s Bathers reveal a new attitude to the relationship between a figure’s size and the picture space it occupies—an attitude which Scully pushes to an absurd extreme in his homage. In Scully’s work, a pun on his own stark “strip” now overwhelms the massive linen in wide vertical navys and ficus greens—trunk-like lines which replace any semblance of real body with pure feeling. To amplify a sense of human weight and depth, Scully has constructed boxy protrusions from the canvas’s surface which invest the work with an air of carpentry and craftsmanship, of things concealed in built cupboards.

The earliest of the oil works on display is a quartet of large canvases collectively entitled Four Dark Mirrors (2002). Each constituent panel is split lengthwise to create a pair of parallel runners or facing vertical fields of clashing horizontal stripes. As a significant subgenre of Scully’s work, mirrors are first discernible as far back as 1983, and while one’s instinct is to read into the collision of different widths and colours a playful philosophical statement on the very enterprise of creative imitation of the physical world, a more intriguing alternative niggles from the atlas of the painter’s biography. The coloration of Four Dark Mirrors is most conspicuously in accord with the watercolour discussed above, Mexico 12.23.83, undertaken the same year as Scully’s first so-called mirror. All three works excavate dense obsidian blacks and warm desert golds which glint mysteriously beside drenched rectangular rags of coagulating red. The scheme is strikingly similar to depictions of an extraordinary incarnation of “mirror” that Scully may well have encountered in his excursions to Mexico—the central deity in the ancient Aztec religion, Tezcatlipoca—whose name is commonly translated as “Smoking Mirror”. In honour of Tezcatlipoca (who was typically depicted in folk art with gold and black stripes across his face), each year an Aztec man was chosen to marry four brides before ascending the steep Templo Mayor, where he was sacrificed by priests and his body was eaten. Seen in this brutally mystical context, the four stark marriages of Scully’s strata are less helpfully compared to reflective cosmetic surfaces, and begin to conjure instead the endlessly eroding steps to Smoking Mirror’s legendary sacrificial temple in Tenochtitlan, as the painter’s work aspires to something beyond the inert mimesis of conventional representationalism to a primitive alchemy capable of transforming the perishable substances of this world into the eternal.

The stakes are just as high in the only other four-panel composition on display in the exhibition, 4 Towers (2009). The work’s title feels at once mythic and architectural, as if alluding to the impenetrable perpendicularity of the medieval Bunratty Castle, whose four broad stone towers still stand formidably in the artist’s native Ireland, or to the two pairs of thinning spires that rise above the Nativity façade of Gaudi’s fragmented Sagrada Familia church in Barcelona—the only four towers of a projected twelve to be completed before the death of the Catalan architect. Scully’s wide totems, each stacking four geometrically precise blocks of rich uninterrupted color (recalling the commercial color chart phases of Ellsworth Kelly or Gerhard Richter), perfect a process—oil on aluminium—that the artist first experimented with in the mid 1990s with a series of ‘floating’ works, which he affixed to the wall at jutting right angles along each panel’s side. Unlike canvas, aluminium resists the easy respiration of color, the breathing between layers of paint—its rigidity serving only to buttress the sense of sturdy aesthetic carpentry. The metallic opacity of the style conducts an entirely different energy through these works, converting them, materially, into panes which reflect back far more than they absorb, like stained glass windows in an abandoned cathedral when a cloud-scarfed moon has turned the sky outside to stone.

"Four Days," 2015 

Now let’s move to the central nave and have a look at the altar cross. Sculpture has been of increasing interest in Scully’s recent work. Aside from two monumental 2007 sculptures, Wall of Light Cubed, made from blocks of colored Portuguese granite, it is only in very recent years that the artist started exploring the three-dimensional possibilities of his language. The altar cross of Santa Cecilia is made of stacked blue glass bricks. The transparent material reveals the bare steel inside that holds it all together like a skeleton. He told me that he wanted to show the hardness and roughness of the cross, and cover it with this soft blue armor, as if to let the motherly and compassionate presence of Mary veil the otherwise unbearable sight. Childhood memories may have oriented him, consciously or not. I once asked him who had the biggest impact on him as an artist. I expected him to answer Rothko, or Matisse, or Cimabue. “My grandmother,” he said without hesitation. He recalled her as a poor, hardworking woman who had several jobs and seven children to care for. She was also “a very devout woman” with “a joyful grasp on life.” The hardness of life, covered by a mantle of faith and joy. He also mentioned in a recent lecture about Santa Cecilia that his grandmother used to make a game of stacking coins, challenging herself to raise the tower as high as possible—an image echoed in the blue glass bricks.





Of all the works inside Santa Cecilia, Holly stands out, not only for its monumental size, but also for its religious atmosphere and austerity. Fourteen insets are embedded in a heavy panel of raw steel: seven painted in light, airy tones make up the upper row; seven in heavy earth tones compose the lower. They represent the fourteen Stations of the Cross, fourteen moments from Jesus’s dramatic ascent up the Golgotha: a human tragedy, as symbolized by the bloody, earthly colors in the lower row; a way of redemption, a triumphant march, as expressed in the heavenly colors above. To the eyes of men, a descent, a kenosis. To the eyes of faith, an ascent, a victory. Each inset is made of two blocks of color, staging a simple, elemental relationship, not unlike Rothko’s late paintings from the sixties, as if to remind us that both passion and redemption originate in relationships: Jesus’s passionate love for humanity and his absolute, filial obedience to the Father. At the bottom of Holly a sentence in Latin is carved in the steel: Languores et luctus humani generis in cruce Christi unde salus, vita, et pax. “The pains and sorrows of mankind focus on the cross of Christ, from whence come health, life, and peace.” From the apse of the Marian chapel, a few steps further and higher, the stained-glass window radiates a deep blue glow that softens the Stations, like a motherly caress.



Shah Walliullah says about evolution, “Human society in its beginning was not much different from animal life but sense and understanding which is present in human beings by nature completed the stages of evolution by mutual cooperation. Human society has never been still at one situation but has been dynamic always.” Human evolution has been a stage- wise action and it is a journey to be completed by stages. With the passage of time, his life goes on becoming better than before. He has divided life from evolutionary point of view into four stages because of characteristics and structure of society.


Four Stages of Society


1. First Stage of Society :

This has been called by Shah Walliullah as first evolution in society. This is a preliminary stage with the following characteristics :

i. Individuals live in small groups and change their residence because of change in weather.


ii. Simple residence, dress and simple way of cooking, utensil, making art living on fruit, vegetables and hunted animals and grain. They knew the art of domestication of animals and

executing work from these animals.


iii. Society is divided into four classes:

a. The wise who suggest for social benefits. A

b. Wealthy class; owner of cattle sheep, land, etc.

c. Brave people to defend society from attacks and dacoits.

d. Cunning people class; desirous of fame, authority and

liking business type activities.


4. Fourth stage of society :

According to Shah Walliullah, “The world is passing through these three stages to reach the fourth stage of complete society with the following characteristics:


i. Collective life being divided into small classes should attach itself to a larger political system to save itself from internal disorders.


ii. Different political unities should create such conditions through mutual cooperation and transfer it to avoid conflict with each other.


According to Shah Walliullah, societies will definitely pass these stages through evolution and the time the society achieves the fourth stage, it will be a complete society which he calls caliphate.



Alfarabi's major work is Book of the opinions of the inhabitants of the righteous city.[32] It is an exposition of a Neo-Platonist emanationist system as well of the different kinds of societies. Alfarabi wanted a perfect city, ruled by a righteous man parallel to the rule of the universe by the perfect One. His connecting cosmogenic explanations and political plans were known to Avempace who did not follow him. Avempace does not quote this or other works by Alfarabi which have a similar content. He quotes Plato but follows the opposite way. While Plato in the Republic would take the human soul as the model for the perfect city, so that the perfect organization inside it tells how the city has to be organized, Avempace starts from the ideal city and wants to transfer its organization to the individual (Abbès 2011, p. 86). Avempace echoes Plato and mentions his division of cities, or societies, into a perfect one and others which are corrupted (Ibn Bâjja 1946, pp. 5–6; 2010, p. 123; Berman 1963, p. 125). One assumes that

Avempace is referring to the four imperfect cities, namely, timocracy, oligarchy, democracy, and tyranny (Republic, viii–ix) although Asín Palacios interpreted them as the four imperfect cities cited in Alfarabi's works (Ibn Bâjja 1946, p. 37, note 6), and Genequand accpts both possibilities (Ibn Bâjja 2010, p. 256).



His original image consisted of the word COEXIST in all capital letters, with the C replaced by an oversized Muslim Crescent, the X replaced by an oversized Star of David, and the T replaced by an oversized Latin Cross.[1][3][2]


One common version of the bumper sticker spells "COEXIST" using an Islamic crescent moon for the "C", a peace sign for the "O", a combination of the male symbol and female symbol for the "E", a Star of David for the "X", a pentagram for the dot of the "I", a yin-yang symbol for the "S", and a Christian cross for the "T".[7] This version, designed by Jerry Jaspar, is perhaps the most common version of the bumper sticker.[8]



The popularity of the bumper stickers has spawned several anti-Muslim responses, including one with the image of the crescent altered with the addition of explosives.[8] Other parodies include a Communist hammer and sickle for the "E" and a swastika for the "X", indicating the dangers inherent in all ideologies.[11]



The Law of Success In Sixteen Lessons by Napoleon Hill Paperback – January 17, 2011


The Law of Success was a precursor to Napoleon Hill's Think and Grow Rich. Hill was well known for researching what made millionaires different from the common man. The sixteen lessons in this book perfectly crystallize everything you will need to know to succeed during these hard economic times. Many of today's best known self help books take there core concepts form this book. The Secret, the Power of Positive Thinking, the Millionaire next door, and The Law of Attraction all take their basic premises from this landmark work. Now you can get it from the source. Once you've read this book you will understand what gives certain people an edge over everyone else. By following the advice laid out clearly herein you'll be the one with an edge. It's time to stop wondering what it's like to be rich and start knowing. This book has changed countless lives and it can change yours! Unlike many of the other editions on the market today, this edition is complete and unabridged! Wilder Publications is a green publisher. All of our books are printed to order. This reduces waste and helps us keep prices low while greatly reducing our impact on the environment.



The Four Motors for Europe are four highly industrialized regions in Europe. It is composed of 1.Milan, Lombardy of Italy; 2.Lyon, Auvergne-Rhône-Alpes of France; 3. Barcelona, Catalonia of Spain; and 4. Stuttgart, Baden-Württemberg of Germany. On September 9, 1988, in Stuttgart, Germany, the presidents of these four territories signed an agreement, called the Memorandum to increase economic and social cooperation between the realms. The agreement was to have the four regions cooperate in a long term relationship in the fields of science, research, education, environment, culture, and other sectors. The purpose of this relationship was to provide a unification force within Europe as well as increasing the potential for economic growth within the four regions. These regions focus on the exchange of information with each other to expand their technology and R&D. Wales and Flanders are also associated with this group.[1]



Auto Union AG, Chemnitz, was an amalgamation of four German automobile manufacturers, founded in 1932 and established in 1936 in Chemnitz, Saxony, during the Great Depression. It is the immediate predecessor of Audi as it is known today.


As well as acting as an umbrella firm for its four constituent brands (Audi, Horch, DKW, Wanderer), Auto Union is widely known for its racing team (Auto Union Rennabteilung, based at Horch works in Zwickau/Saxony). The Silver Arrows of these two German teams (Mercedes-Benz and Auto Union) dominated not only GP car racing from 1934 onwards but set records that would take decades to beat, such as the fastest speed ever attained on a public road (at 432.7 km/h (268.9 mph), unbroken as of 2013).[3] After being reduced to near ruin in the aftermath of World War II, Auto Union was re-founded in Ingolstadt, Bavaria in 1949, ultimately evolving into the modern day Audi company following its takeover by Volkswagen in 1964 and later merger with NSU Motorenwerke in 1969.


The current corporate entity which bears the Auto Union name – Auto Union GmbH – was founded in 1985 and is a wholly owned subsidiary of Audi AG; its purpose is to act as owner of Auto Union's historical trademarks and intellectual property, as well as managing Audi's heritage operations. The company's distinctive logo, of four interlocking rings to represent the original four members of the Auto Union, survives as the logo of Audi.


The trademark symbol of Auto Union (and present-day Audi), the four overlapping rings, symbolized the four marques forming Auto Union: Audi, DKW, Horch, and Wanderer.[19][20]


Although Auto Union used the four ring logo, it was only used on Auto Union racing cars in that period, while the member companies used their own names and emblems.


There is also a version of logo that uses both overlapping and interlocking rings.[21]



One of the first things that Simon does that depicts a Christ-like action, is found in chapter 3 when he helps the littluns get fruit, "Simon found for them the fruit they could not reach" (Golding 56). During his lifetime, Jesus often aided the hungry, one example being when he turned 5 loaves of bread and 2 fish into enough food for thousands of people. Later in the chapter Simon finds himself in the wilderness. While there, Simon was calm and enjoyed the solitude of his surroundings; "He came at …show more content…

From this, he reaches an epiphany and later leaves to tell the other boys. While returning to tell the boys, Simon is hit in the side by a spear. Jesus was also stabbed in the side before his crucifixion.




A quadracycle is a four-wheeled human-powered land vehicle. It is also referred to as a quadricycle, quadcycle, pedal car or four-wheeled bicycle amongst other terms.


There is no consensus amongst manufacturers of four-wheeled, human-powered vehicles as to what this class of vehicles should be called, although quadracycle is the most commonly used term. Manufacturers who do refer to their products by class of vehicle call them:


Quadracycle - 11 manufacturers[2][3][4][5][6][7][8][9]

Four-wheel bicycle - 7 manufacturers[10][11][12][13][14][15][16]

Quadricycle - 5 manufacturers[1][8][16][17][18]

Quadcycle - 3 manufacturers[19][20][21]

Pedal car - 2 manufacturers[22][23]

Quad - 2 manufacturers[24][25]

Quadracycle use diminished in the late 19th century as a result of improvements in bicycle technology that made their four-wheel cousins largely obsolete, although small numbers were manufactured through the 1950s for rental use in tourist areas.


A modern touring 4-wheel bike - a 2011 model Quattrocycle four seater with canopy[33]


The four classical Elemental Powers of EarthFireWater, and Air/Wind usually appear simultaneously inside the same setting. It is tacitly acknowledged these are the four forces of nature, and so naturally, there is some form of magical ability associated with each of them. Sometimes mages are restricted to only one school.


But wait - what's all this talk about a mysterious fifth element? That's right, boys and girls, turns out there's actually another element on top of these that is so incredibly badass, it defies the normal classification system. Magic of this element is about as strong as the other four put together. Where a wind mage has control of, in general, wind, this element controls pretty much everything. It will have very few restrictions, but it will also be quite difficult to use. If the normal magic system is defined in term of Elemental Rock-Paper-Scissors, Element Number Five will usually exist outside of it. Sometimes it will actually be the source of all the other elements in the first place, making it more of a Zero-th element or if you prefer, the element of the elements.


Another common variation is for this to be some kind of mental, spiritual, or energy-related foil to the physical elements; The Power of LoveMind Control, and Light 'em Up are all common choices. The above rules may still apply (especially if the hero or the villain are the ones using it), but non-omniscient powers are equally likely to be balanced as not. The Inverse Law of Complexity to Power often favors Element Number Five since it doesn't always fit the same system as the rest.


Is most commonly used as a distinguishing feature from fantasy work to fantasy work. In order to combat the relative commonality of this fifth element its nature will often vary, to the point that this trope can often turn into Our Fifth Element Is Different.


In spite of the name, this trope can also be another number- the Chinese elemental system, for example, normally contains five elements (Earth, Fire, Water, Metal, and Wood), so in works based on that mythology this will be Element Number Six. This trope occurs naturally in the Greek, Tibetan, Babylonian and Japanese elemental systems, where Aether, Space, Sky and Void fulfill the narrative role of this trope - note that these four are essentially the same thing.


Not to be confused with Boron, the fifth element in the Real Life periodic table; The Fifth Element, which uses this trope as its eponymous Plot Device; or The Fifth Elephant, which has nothing to do with any of this but is rather a cheap pun.


See Infinity +1 Element for the gameplay ramifications of this trope occurring in Video Games.



An ancient tradition holds that Pythagoras discovered the secrets of harmony within a forge when he came across five men hammering with five hammers, producing a wondrous sound. Four of the five hammers stood in a marvelous set of proportions, harmonizing; but there was also a fifth hammer. Pythagoras saw and heard it, but he could not measure it; nor could he understand its discordant sound. Pythagoras therefore discarded it. What was this hammer, such that Pythagoras chose so decidedly to reject it?


Gaffurius, Theorica musicae (1492): Pythagoras exploring harmony and ratio with various musical instruments




According to legend, Pythagoras discovered the foundations of musical tuning by listening to the sounds of four blacksmith's hammers, which produced consonance and dissonance when they were struck simultaneously. According to Nicomachus in his 2nd century CE Enchiridion harmonices [1] Pythagoras noticed that hammer A produced consonance with hammer B when they were struck together, and hammer C produced consonance with hammer A, but hammers B and C produced dissonance with each other. Hammer D produced such perfect consonance with hammer A that they seemed to be "singing" the same note. Pythagoras rushed into the blacksmith shop to discover why, and found that the explanation was in the weight ratios. The hammers weighed 12, 9, 8, and 6 pounds respectively. Hammers A and D were in a ratio of 2:1, which is the ratio of the octave. Hammers B and C weighed 9 and 8 pounds. Their ratios with hammer A were (12:9 = 4:3 = perfect fourth) and (12:8 = 3:2 = perfect fifth). The space between B and C is a ratio of 9:8, which is equal to the musical whole tone, or whole step interval.


Ontong Java–Manihiki–Hikurangi Plateau121 Southwest Pacific Ocean59–77[n 5]Largest igneous body on Earth, later split into three widely separated oceanic plateaus, with a fourth component perhaps now accreted onto South America. Possibly linked to the Louisville hotspot.




FIA Formula 4, also called FIA F4, is an open-wheel racing car category intended for junior drivers. There is no global championship, but rather individual nations or regions can host their own championships in compliance with a universal set of rules and specifications.



A three-body problem also arises from the situation of a spacecraft and two relevant celestial bodies, e.g. the Earth and the Moon, such as when considering a free return trajectory around the Moon, or other trans-lunar injection. While a spaceflight involving a gravity assist tends to be at least a four-body problem (spacecraft, Earth, Sun, Moon), once far away from the Earth when Earth's gravity becomes negligible, it is approximately a three-body problem.


Mars has four known co-orbital asteroids (5261 Eureka, 1999 UJ7, 1998 VF31, and 2007 NS2, all at the Lagrangian points)



The new UCLA campus in 1929 had four buildings: Royce Hall and Haines Hall on the north, and Powell Library and Kinsey Hall (now the Humanities Building) on the south. The Janss Steps were the original 87-step entrance to the university that lead to the quad of these four buildings. Today, the campus includes 163 buildings across 419 acres (1.7 km²) in the western part of Los Angeles, north of the Westwood shopping district and just south of Sunset Boulevard. In terms of acreage, it is the second smallest of the ten UC campuses.[7] The campus is close but not adjacent to the 405 San Diego Freeway.[40]


The original four buildings were the College Library (now Powell Library), Royce Hall, the Physics-Biology Building (now the Humanities Building), and the Chemistry Building (now Haines Hall), arrayed around a quadrangular courtyard on the 400 acre (1.6 km²) campus. The first undergraduate classes on the new campus were held in 1929 with 5,500 students. After lobbying by alumni, faculty, administration and community leaders, UCLA was permitted to award the master's degree in 1933, and the doctorate in 1936, against continued resistance from UC Berkeley.[34]


The first buildings were designed by the local firm Allison & Allison. The Romanesque Revival style of these first four structures remained the predominant building style until the 1950s, when architect Welton Becket was hired to supervise the expansion of the campus over the next two decades


The Associated Students UCLA (ASUCLA) encompasses the student government and student-led enterprises at UCLA. ASUCLA has four major components: the Undergraduate Students Association, the Graduate Students Association, Student Media, and services & enterprises.


There are four type of housing available for students: residential halls, deluxe residential halls, residential plazas, and residential suites. Available on the hill are study rooms, basketball courts, tennis courts, and Sunset Recreational Center which includes three swimming pools.

Examples of the Magic Square and Temple Design

 A. The Villa Capri  - Andrea Palladio, 1566

B. The Pantheon, 1790 

C.  Brammante, Da Vinci, and the Quincunx,  975 - 1506

The Magic Square, the Moon, the Swastika, and the Quincunx



This example of a Greek coin from Knossos, c 350 BC, seems to incorporate the 3x3 magic square, the symbol for the moon, and the swastika.

The Greek coin with the swastika has the number five as its center, or axis mundi. The number five at the center of a cross – in – square pattern with four similar quadrants makes a strong correspondence to the 3x3 magic square. The four quadrants have the symbol for the moon and the four cardinal directions correspond to the arms of the swastika. The quincunx can be seen as the axis mundi as well as the four moons around the center or the four arms of the swastika around the center. The coin also exhibits the circle and square relationship, that is, a square 3x3 grid inside a circular coin.


Agrippa's magical sigil for the moon also has a quincunx pattern around its center or axis mundi. The four arms pointing in the four cardinal directions also create the four quadrants where the symbol for the moon resides and just as in the Greek coin from Knossos the crescent moon is pointing in the same direction. Four circles at the end of each arm form a quincunx with the center circle. The sigil also demonstrates the circle and square relationship and corresponds with the 9x9 magic square.


The 9x9 magic square demonstrates a cross – in – square pattern as only odd numbers occupy the horizontal and vertical axis. The center or axis mundi is represented by the number 41 as this is the center between 9 and 92 just as the number five is the center number between 3 and 32.







Numbers represented a language that helped to connect humankind to the Heavens. The magic square helps to unravel this language.


Another use of the magic square in art was in the form of geometric symbolism rather than an explicit square of numbers. This was a subtle representation as the cognitive use of the magic square was not intended for the common person.


The magic square was used in art in the form of the quincunx, known as sacred geometry, a pattern that was symbolic of a universal cosmology.




This universal cosmology does not have a known origin. The early Chinese of more than three thousand years ago developed the Luo Shu into a model that represented their cosmology, as documented in the Yi Jing.


The Luo Shu represented a perfect balance of Yin and Yang as the even numbers symbolized female and yin energy, the earth, and the four intermediate directions. The number four symbolized the four elements: air, water, earth, and fire. The four quadrants of the magic square symbolized the earth. The “square” earth was a reference to measuring the earth with a carpenter’s square and the Pythagorean Theorem.


The cross of odd numbers symbolized male and yang energy, Heaven, and the four cardinal directions. The circular nature of Heaven encapsulates the earth and is represented by the compass and circle. In temple and church design this concept is illustrated as the circular dome (omphalos) is placed over a square base.


The Center


The center is the most important concept in Chinese cosmology; also known as the axis mundi (Latin). The center number five is surrounded by four odd and four even numbers for a perfect balance. In the ground plan of early church design the axis mundi symbolized the convergence of Heaven, earth, the transcended human, and corresponded to the central dome and altar (and sometimes a tomb).


The odd and even numbers (sans the number five) are in a quincuncial relationship with the number five, i.e., the center. This quincunx of numbers can be translated into a geometric representation using the square and circle:



Detail of the Ambassadors Depart (c. 1498) by Vittore Carapaccio





This sacred geometrical pattern is modeled after the Luo Shu and represents a cosmology that explains the universe.


This pattern is known as the quincunx and was used to identify places or things of political or religious importance.





The Cosmology of the Quincunx: The Circle and Square


The quincunx was the most popular ground plan for churches in the middle Byzantine era. The quincunx pattern has been commonly used on the covers of the most sacred books, both in church art and for real. And the quincunx was a favorite pattern of the Cosmati pavements in dozens of the oldest Italian churches. The pattern was used with intention to mark the most revered places or items of religious or political significance because the quincunx encompassed all the elements that could explain the universe.



The quincunx church

"The center symbolizes the beginning, the origin, the starting point, the pure being, the absolute, the transcendent, in three dimensions, the center corresponds to the axis, which unites a point with the zenith (the North Star), indicating verticality. The circle - in space, the sphere - represents the infinite, transcendent, and complete, in sum, the divine, god. The square – in space, the cube – is the symbol of the earth, connected in its order to the four cardinal points. The cross marks the four points of the compass; it stems from joining the center with each one of the points, establishing the orientation of the point in space and in time. The cross is the mediating symbol that connects heaven and earth."

Paloma Pajares Ayuela, Cosmatesque Ornament (2001)






1. Altar cloth, c. 450 AD

2. Lindau Gospels, c. 875 AD

3. Cosmati Pavement, c. 1150 - 1350 AD

4. Church drawing, Da Vinci, c. 1485 AD

5. The Ambassadors Depart c. 1498 AD

HE TU number map



In classical Feng Shui, the He Tu combination of numbers embody the YIN and YANG pairings of the five elements. The He Tu numbers are derived from the Map of compass primary directions; North, South, East and West are represented by a He Tu pair of numbers.

He Tu Number relations

The numbers 1 and 6 reside in the North

The numbers 2 and 7 reside in the South

The numbers 3 and 8 reside in the East

The numbers 4 and 9 reside in the West

In addition to the above four pairs of numbers, 5 & 10 are said to represent earth energy residing in the centre. The odd numbers are YANG numbers, while the even numbers are YIN numbers. The He Tu pattern is illustrated in the diagram shown below.

1 and 6 are water elements.

2 and 7 are fire elements.

3 and 8 are wood elements.

4 and 9 are metal elements.

Running in a clockwise direction starting from the centre (Earth), the combinations flow as in the Productive cycle; Earth [5 & 10] produces Metal [4 & 9], Metal produces Water [1 & 6], Water nourishes Wood [3 & 8], Wood nourishes Fire [2 & 7], Fire produces Earth.



A number which is a harshad number in every number base is called an all-harshad number, or an all-Niven number. There are only four all-harshad numbers: 1, 2, 4, and 6 (The number 12 is a harshad number in all bases except octal).




The puzzle that Fibonacci posed was: how many pairs will there be in one I year?


At the end of the first month, they mate, but there is still only 1 pair.

At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.

At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.

At the end of the fourth month, the original female has produced yet another new pair, and the female born two months ago also produces her first pair, making 5 pairs.

At the end of the nth month, the number of pairs of rabbits is equal to the number of new pairs (which is the number of pairs in month n − 2) plus the number of pairs alive last month (n − 1). This is the nth Fibonacci number.[16]


The name "Fibonacci sequence" was first used by the 19th-century number theorist Édouard Lucas.[17]



In the Campus Martius, many public monuments had a religious significance, as they were temples to various gods that were absorbed into the Roman culture. One of the biggest monuments is the temple of Mars Ultor (the avenger) dedicated to Mars, the god of War. It is in the Forum Augustum and is Augustus’s most ambitious architectural building. The construction started in 30BC and took three decades. The exterior of the temple was constructed using the Italian white Luna marble from Carrara[36] and the columns reflect the Corinthians style. The architecture is strongly influenced by the Temple of Jupiter Capitolinus in terms of its dimensions (36 meters wide and its length is 50 meters.[36] It was also a political entity aimed at magnifying Augustus role in avenging Caesar’s assassination.


Some of the most significant temples of the campus are the rectangular temples of Largo di Torre Argentina, located in the southern part of the Campus Martius. It is a religious complex composed of four temples: Temple Juturna, Temple Fortuna Huiusce Diei, Temple Feronia, and Temple Lares Permarini. Those temples demonstrate that religious activity is being spread out across Rome and is not focused on the former religious places of the Capitoline Hill or the Forum Romanum.[36] Art historian Stamper argues that the Largo Argentina has marked the beginning of multiple triumphal processions of successful generals. During the 1st century BC, there was a change from the Ionic style to the Corinthian Order. Acanthus leaves were sculpted on the top of these columns.[36]



Largo di Torre Argentina is a square in Rome, Italy, with four roman Republican temples and the remains of Pompey's Theatre. It is in the ancient Campus Martius.[1]


After Italian unification, it was decided to reconstruct part of Rome (1909), demolishing the zone of Torre Argentina. However, during the demolition work in 1927, the colossal head and arms of a marble statue were discovered. The archeological investigation brought to light the presence of a holy area, dating to the Republican era, with four temples and part of Pompey's Theater.


The four temples, originally designated by the letters A, B, C, and D, front onto a paved street, which was reconstructed in the imperial era, after the fire of AD 80. The area was delineated to the North by the Hecatostylum (one-hundred columns porch) and the Baths of Agrippa, and to the South by the buildings related to the Circus Flaminius, to the East by the great porched square of Porticus Minucia Frumentaria, and to the West by the Theatre of Pompey.[3][4]


Temple A was built in the 3rd century BC, and is probably the Temple of Juturna built by Gaius Lutatius Catulus after his victory against the Carthaginians in 241 BC.[5] It was later rebuilt into a church, whose apse is still present.


Temple B, a circular temple (tholus) with six columns remaining, was built by Quintus Lutatius Catulus in 101 BC in fulfillment of his vow at the Battle of Vercellae.[6] The temple (aedes) was devoted to Fortuna Huiusce Diei, "the Fortune of This Day." The colossal statue found during excavations and now kept in the Capitoline Museums was the statue of the goddess herself. Only the head, the arms, and the legs were made of marble: the other parts, covered by the dress, were of other materials, probably a wooden frame. This is known as an acrolithic statue.



Detail of portrait head of Fortuna huiusce diei

Temple C is the most ancient of the three, dating back to 4th or 3rd century BC, and was probably devoted to Feronia the ancient Italic goddess of fertility. After the fire of 80 AD, this temple was restored, and the white and black mosaic of the inner temple cell dates back to this restoration.


Temple D is the largest of the four, dates back to 2nd century BC with Late Republican restorations, and was devoted to Lares Permarini (Lares who protect sailors), but only a small part of it has been excavated (a street covers the most of it). It was vowed by the praetor, Lucius Aemilius Regillus, while engaged in a naval battle with the fleet of Antiochus the Great in 190 B.C., and dedicated by M. Aemilius Lepidus, when censor, on 22 December, 179.[7] On the doors of the temple was a dedicatory inscription in Saturnian metre.[8] It is recorded as standing in porticu Minucia[9] and therefore its exact site depends on that of the porticus.[10][11]



The Iowa-class battleships were a class of six fast battleships ordered by the United States Navy in 1939 and 1940 to escort the Fast Carrier Task Forces that would operate in the Pacific Theater of World War II. Four were completed, two more were laid down but canceled in August 1945, at war's end, and both hulls were scrapped in 1958. Like other third-generation American battleships, the Iowas followed the design pattern set forth in the preceding North Carolina-class and South Dakota-class battleships, which emphasized speed in addition to secondary and anti-aircraft batteries.[1] Based on wartime experience, they were to serve as fast escorts for Essex-class aircraft carriers.


Between the mid-1940s and the early 1990s, the Iowa-class battleships fought in four major US wars. In World War II, they defended aircraft carriers and shelled Japanese positions. During the Korean War, the battleships provided seaborne artillery support for United Nations forces fighting North Korea, and in 1968, New Jersey shelled Viet Cong and Vietnam People's Army forces in the Vietnam War. All four were reactivated and modernized at the direction of Congress in 1981, and armed with missiles during the 1980s, as part of the 600-ship Navy initiative. During Operation Desert Storm in 1991, Missouri and Wisconsin fired missiles and 16-inch (406 mm) guns at Iraqi targets.


The Navy had spent about $1.7 billion, from 1981 through 1988, to modernize and reactivate the four Iowa class battleships. Costly to maintain, the battleships were decommissioned during the post-Cold War draw down in the early 1990s. All four were initially removed from the Naval Vessel Register; however, the United States Congress compelled the Navy to reinstate two of them on the grounds that existing naval gunfire support would be inadequate for amphibious operations. This resulted in a lengthy naval gunfire debate over whether battleships should have a role in the modern navy. Ultimately, all four ships were stricken from the Naval Vessel Register and released for donation to non-profit organizations. With the transfer of Iowa in 2012, all four are part of various non-profit maritime museums across the US.



The world's supply of titanium metal, about 250,000 tons per year, is made from TiCl4. The conversion takes place by the reduction of the chloride with magnesium metal, and yields titanium metal and magnesium chloride. This procedure is known as the Kroll process:[6]


2 Mg + TiCl4 → 2 MgCl2 + Ti

Liquid sodium has also been used instead of magnesium as the reducing agent, as in the Hunter process.




Titanium tetrachloride is the inorganic compound with the formula TiCl4. It is an important intermediate in the production of titanium metal and the pigment titanium dioxide. TiCl4 is an unusual example of a metal halide that is highly volatile. Upon contact with humid air, it forms spectacular opaque clouds of titanium dioxide (TiO2) and hydrogen chloride (HCl). It is sometimes referred to as "tickle" due to the phonetic resemblance of its molecular formula (TiCl4) to the word.[2][3]



Parasympathetic ganglia are the autonomic ganglia of the parasympathetic nervous system. Most are small terminal ganglia or intramural ganglia, so named because they lie near or within (respectively) the organs they innervate. The exceptions are the four paired parasympathetic ganglia of the head and neck.


These paired ganglia supply all parasympathetic innervation to the head and neck.


ciliary ganglion (sphincter pupillae, ciliary muscle)

pterygopalatine ganglion (lacrimal gland, glands of nasal cavity)

submandibular ganglion (submandibular and sublingual glands)

otic ganglion (parotid gland)



In enzymology, an adenosine-tetraphosphatase (EC is an enzyme that catalyzes the chemical reaction


adenosine 5'-tetraphosphate + H2O

⇌\rightleftharpoons ATP + phosphate

Thus, the two substrates of this enzyme are adenosine 5'-tetraphosphate and H2O, whereas its two products are ATP and phosphate.


This enzyme belongs to the family of hydrolases, specifically those acting on acid anhydrides in phosphorus-containing anhydrides. The systematic name of this enzyme class is adenosine-tetraphosphate phosphohydrolase. This enzyme participates in purine metabolism.



Adenosine 5'-tetraphosphate is a nucleotide. It is produced from ATP and triphosphate (P3) through the action of acetyl—CoA synthetase.[1] Acetyl—CoA synthetase also produces adenosine 5'-pentaphosphate through the reaction of ADP and tetraphosphate (P4). Its current function is unknown.


There are only four layers in the epidermis of thin skin. The stratum lucidum layer is absent.



Skin that has four layers of cells is referred to as “thin skin.” From deep to superficial, these layers are the stratum basale, stratum spinosum, stratum granulosum, and stratum corneum. Most of the skin can be classified as thin skin.



Within the somatosensory system, there are four main types of receptors: mechanoreceptors, thermoreceptors, pain receptors, and proprioceptors.



A four-planet system in orbit, directly imaged and remarkable


The era of directly imaging exoplanets has only just begun, but the science and viewing pleasures to come are appealingly apparent.


This evocative movie of four planets more massive than Jupiter orbiting the young star HR 8799 is a composite of sorts, including images taken over seven years at the W.M. Keck observatory in Hawaii.


The movie clearly doesn’t show full orbits, which will take many more years to collect. The closest-in planet circles the star in around 40 years; the furthest takes more than 400 years.


But as described by Jason Wang, an astronomy graduate student at the University of California, Berkeley, researchers think that the four planets may well be in resonance with each other.


In this case it’s a one-two-four-eight resonance, meaning that each planet has an orbital period in nearly precise ratio with the others in the system.


The black circle in the center of the image is part of the observing and analyzing effort to block the blinding light of the star, and thus make the planets visible.


The images were initially captured by Dr. Christian Marois of the National Research Council of Canada’s Herzberg Institute of Astrophysics. The movie animation was put together by Wang, who is part of the Berkeley arm of the Nexus for Exoplanet System Science (NExSS), a NASA-sponsored group formed to encourage interdisciplinary exoplanet science.


The star HR 8799 has already played a pioneering role in the evolution of direct imaging of exoplanets. In 2008, the Marois group announced discovery of three of the four HR 8799 planets using direct imaging for the first time. On the same day that a different team announced the direct imaging of a planet orbiting the star Fomalhaut.


HR 8799 is 129 light-years away in the constellation of Pegasus. By coincidence, it is quite close to the star 51 Pegasi, where the first exoplanet was detected in 1995. It is less than 60 million years old, Wang said, and is almost five times brighter than the sun.


Wang said that the animation is based on eight observations of the planets since 2009. He then used a motion interpolation algorithm to draw the orbit between those points.


Much can be learned from the motion of the planets, however long it may take for them to circle their sun. Based on the Keck observations, astronomers have concluded that the four planets orbit in roughly Keplerian motion around the star — almost circular, but not entirely.


The planets are quite far from each other, which is to be expected due to their enormous size. Because of those large separations, Wang said astronomers will be watching to see if the system is stable or if some of the planets may be ejected from the system.


Although the first three HR 8799 planets were officially discovered in 2008, researchers learned afterwards that the planets had actually already been observed. The “precovery” had been made in 1998 by the NICMOS instrument on the Hubble Space Telescope, but was teased out only after a newly developed image-processing technique was installed.


The fourth HR 8799 planet was found after further observations in 2009–2010. That planet orbits inside the first three planets, but is still fifteen times the distance from its star than Earth to our sun. (The team working with Marois included Quinn Konopacky of the University of California, San Diego, Bruce Macintosh of Stanford University and Travis Barman of the University of Arizona.)


James Graham is leader of the Berkeley NExSS group, and he was struck by some of the connections between what has been found around HR 8799 and what exists in our own solar system.



The earliest Sumerian literature of the third millennium BC identifies four primary deities: An, Enlil, Ninhursag, and Enki. These early deities were believed to occasionally behave mischievously towards each other, but were generally viewed as being involved in co-operative creative ordering.[15]



The Hanbali school is now accepted as the fourth of the mainstream Sunni schools of law. It has traditionally enjoyed a smaller following than the other schools. In the earlier period, Sunni jurisprudence was based on four other schools: Hanafi, Maliki, Shafi'i and Zahiri; later on, the Hanbali school supplanted the Zahiri school's spot as the fourth mainstream school.[33] Hanbalism essentially formed as a traditionalist reaction to what they viewed as speculative innovations on the part of the earlier established schools.[34]


Eventually, the Mamluk Sultanate and later the Ottoman Empire codified Sunni Islam as four schools, including the Hanbalite school at the expense of the Zahirites.[38][39] The Hanafis, Shafi'is and Malikis agreed on important matters and recognized each other's systems as equally valid; this was not the case with the Hanbalites, who were recognized as legitimate by the older three schools but refused to return the favor.[34]



As a result of improvements Galileo Galilei made to the telescope, with a magnifying capability of 20×,[4] he was able to see celestial bodies more distinctly than was ever possible before. This allowed Galilei to discover in either December 1609 or January 1610 what came to be known as the Galilean moons.[2][5]


On January 7, 1610, Galileo wrote a letter containing the first mention of Jupiter's moons. At the time, he saw only three of them, and he believed them to be fixed stars near Jupiter. He continued to observe these celestial orbs from January 8 to March 2, 1610. In these observations, he discovered a fourth body, and also observed that the four were not fixed stars, but rather were orbiting Jupiter.[2]


Galileo asked whether he should name the moons the "Cosmian Stars", after Cosimo alone, or the "Medician Stars", which would honor all four brothers in the Medici clan. The secretary replied that the latter name would be best.[2]


On March 12, 1610, Galileo wrote his dedicatory letter to the Duke of Tuscany, and the next day sent a copy to the Grand Duke, hoping to obtain the Grand Duke's support as quickly as possible. On March 19, he sent the telescope he had used to first view Jupiter's moons to the Grand Duke, along with an official copy of Sidereus Nuncius (The Starry Messenger) that, following the secretary's advice, named the four moons the Medician Stars.[2] In his dedicatory introduction, Galileo wrote:


Scarcely have the immortal graces of your soul begun to shine forth on earth than bright stars offer themselves in the heavens which, like tongues, will speak of and celebrate your most excellent virtues for all time. Behold, therefore, four stars reserved for your illustrious name ... which ... make their journeys and orbits with a marvelous speed around the star of Jupiter ... like children of the same family ... Indeed, it appears the Maker of the Stars himself, by clear arguments, admonished me to call these new planets by the illustrious name of Your Highness before all others.[2]


Fluctuations in the orbits of the moons indicate that their mean density decreases with distance from Jupiter. Callisto, the outermost and least dense of the four, has a density intermediate between ice and rock whereas Io, the innermost and densest moon, has a density intermediate between rock and iron. Callisto has an ancient, heavily cratered and unaltered ice surface and the way it rotates indicates that its density is equally distributed, suggesting that it has no rocky or metallic core but consists of a homogeneous mix of rock and ice. This may well have been the original structure of all the moons. The rotation of the three inner moons, in contrast, indicates differentiation of their interiors with denser matter at the core and lighter matter above. They also reveal significant alteration of the surface. Ganymede reveals past tectonic movement of the ice surface which required partial melting of subsurface layers. Europa reveals more dynamic and recent movement of this nature, suggesting a thinner ice crust. Finally, Io, the innermost moon, has a sulfur surface, active volcanism and no sign of ice. All this evidence suggests that the nearer a moon is to Jupiter the hotter its interior. The current model is that the moons experience tidal heating as a result of the gravitational field of Jupiter in inverse proportion to the square of their distance from the giant planet. In all but Callisto this will have melted the interior ice, allowing rock and iron to sink to the interior and water to cover the surface. In Ganymede a thick and solid ice crust then formed. In warmer Europa a thinner more easily broken crust formed. In Io the heating is so extreme that all the rock has melted and water has long ago boiled out into space.



Zoroaster's teachings, a general res- urrection will take place at the end of the present world. The good and

evil will then be sub- jected to an ordeal of fire and molten metal. By this fiery test the evil will be made known by

their terrible burning, but the righteous will find the fire kindly and the molten metal harmless. The world's his- tory is therefore nothing but the story of the contest be- tween good and evil which shall endure for 12,000 years, divided into four equal periods of 3,000 years. The fi- nal aim of Zoroaster's system is to assure world perfec- tion by the individual's adoption of the right path.



According to Vuibert (12), Magism was the reli- gion of the various Scythic tribes which inhabited the mountain range of Armenia, Azerbijan, Kurdistan, and Luristan. Its chief objects of worship were air, water, earth, and fire. It was to these elements, to the actual material things themselves, that adoration was paid. Fire, as the most subtle and ethereal principle, was held in the highest reverence



Zoroastrian cosmology is divided in four periods of 3,000 years. Zoroaster was born in the beginning of the fourth period, to be succeeded at the end of each next millennium by a new saviour.



Antoine Lavoisier (1743-1794) introduced the system of chemical nomenclature. His Traité Élémentaire de Chimie (1789) was the first modern chemical textbook, and presented a unified view of new theories of chemistry. In addition, it contained a list of 33 elements, or substances that could not be broken down further. His list also included light (lumière) and caloric (calorique), which he believed to be material substances. Lavoisier himself grouped them into four categories on the basis of their chemical properties:

Simple substances belonging to all the kingdoms of nature, which may be considered as the elements of bodies (gases),

Oxidable and Acidifiable simple Substances not Metallic (nonmetals),

Oxidable and Acidifiable simple Metallic Bodies (metals),

Salifiable simple Earthy Substances (earths).


Resource theory represents human relationships and interaction as methods for providing people with six social resources: love, services, goods, money, information and status. Each resource can be exchanged for another, or people can reciprocally exchange the same resource. The possibilities are often illustrated by an encircled hexagon, with each of resources labelling a vertex, and all of the vertices connected to all the others by lines. Around this circle a box is drawn, and the four sides of the box are labelled, in terms that describe the structure of concern (Foa et al., 1993; Foa, 1993).


The dimensions are described as high-low concreteness dimension (or concrete-symbolic), and a high-low particularistic dimension (particularistic-universal). Exchanges of goods and services are concrete, exchanges of information and status interactions are more symbolic. We are very particular about who we give and receive love with, but we’ll exchange money with anyone in a marketplace without cheapening or degrading the value of that money.


In PAEI terms, P is concrete and E is symbolic, while I is particular and A universal. On this account therefore, P and E differ along a “what” dimension regarding goals and rewards, while I and A differ along a “who” dimension of people to whom the interactive pattern applies. Resource preferences of the four different PAEI style could be described thusly:


P – High Concreteness: Focus on tangible acquisitions. Preferred resources: goods and services.

A – Low Particularism: Focus on standard, universal, generic exchanges. Preferred resources: money, followed by information and goods.

E – Low Concreteness: Focus on symbolism. Preferred resources: information and status.

I – High Particularism: Focus on interpersonal interactions. Preferred resources: love, followed by services and status.


Lawrence and Nohria are professors of organizational behavior at the Harvard Business School who felt dissatisfied with the rather featureless construct of homo economicus as a rational maximizer. Humans are clearly motivated by more than personal self-interest, even in their economic behavior. The authors point to the colossal failure of neoclassical economic reforms in Russia as one devastating example of how human behavior is clearly driven by factors that neoclassical theory does not see. The authors turned to evolutionary biology and neuroscience to construct a more complete model of basic human nature (Lawrence & Nohria, 2002).


As the outcome of their research, the authors postulate a fundamental basis for human behavior composed of four distinct drives, listed below in PAEI order:


P – (D1) The drive to acquire

A – (D4) The drive to defend

E – (D3) The drive to learn

I – (D2) The drive to bond


These may not be the only human drives, but they are the only ones necessary and sufficient for constructing a “unified understanding of modern human life”. The four drives motivate and direct human action, perception, cognition/reasoning and memory/representation. They are all independent drives with limbic origins but they exert their effects through the tightly integrated work of the prefrontal cortex.


The emergence of this prefrontal coordination coincides with the cognitive Great Leap Forward in human cultural sophistication during the Upper Paleolithic era. Lawrence and Nohria discuss the implications of their findings for organizational management.


Charles Perrow’s Normal Accident Theory is difficult to situate in this catalog because it is a sociological tool, a management tool and a systems analysis and design tool all in equal measure. His theory targets the intersection between complex technological systems and human management practices. Some specific targets of his analysis are high-risk enterprises using high-risk technologies, such as nuclear power plants, petrochemical plants, supertankers, major airport systems, hydroelectric dams and the like – systems with high catastrophic potential. However, in discussing what differentiates these systems from less risky systems, he creates a general typology of systems. This typology names dimensions that I believe lie near the core of the structure of concern (Perrow, 1999).


Perrow argues that there is a particular class of accidents that are normal, inevitable, and are often potentially disastrous. These occur in systems with many components, complex interconnections, strict dependencies and stringent performance conditions. In systems like this, it is computationally impossible to foresee all of the failures that might happen. One also cannot tell how failures might compound each other if two or more were to happen simultaneously. Between design limitations, equipment failures, procedural errors, operator error, problems in supplies and materials, and unknown variables in the environment (Perrow calls this set of considerations DEPOSE), there will always be unforeseen complications and unexpected contingencies. Plus when multiple factors combine to produce accidents in such systems, it will rarely if ever be possible to figure out what is going on in real time. Only post-mortem analysis will reveal the failure path.


Systems that are prone to normal accidents can be identified by their interactive complexity and the coupling relationships among their components. Interactions in a system (across all DEPOSE elements) can be linear or complex. For linear interactions, there is an expected sequence for events along the main causal pathways, and even if unexpected and unplanned events occur, they are immediately visible by the way they cause the system to deviate from its expected functions. Complex interactions occur in unfamiliar, unplanned, unexpected and unforeseeable sequences. Problems, flaws or failures in complex interactions are not visible, and often cannot be comprehended as they unfold. This is because there are multiple elements from across the DEPOSE system interacting simultaneously to produce unpredictable results during complex interactions.


One important source of complexity is called common-mode functioning. In complex systems, some components perform multiple functions (e.g. a wall both holds up the roof and keeps out the wind). This improves design economy, and it reduces certain kinds of complexity, but the failure of common-mode components will be more serious when they happen, bringing non-linearity into the system. A small initial accident that slightly damages a common-mode element can have huge unforeseen consequences, depending on what else is happening in the system. Cause and effect will not be proportionate.


Note that these observations apply to interactions within systems, rather than to systems themselves. Perrow asserts that linear interactions predominate in all systems, but some systems permit more complex interaction than others. Furthermore, complex interactions themselves are not necessarily likely to cause accidents. A second dimension must be considered, namely the tightness or looseness of coupling between the DEPOSE components or subsystems of the system. In tightly coupled systems, there is little or no slack or buffering between the various interconnected components. What happens to one component directly affects what happens to other components around it and connected to it. Chain-reactions or domino-effects happen easily in tightly coupled systems. Loosely coupled systems do have buffers and slack. Components have a certain amount of functional autonomy from each other. Systems characterized by both complex and tightly coupled interactions are prone to normal accidents.


Crossing the dimensions of interactive complexity and coupling give us four categories of interaction: linear tight, linear loose, complex tight, complex loose. This sequence of the four categories is in PAIE order, rather than PAEI order. However, PAIE order does match the account of the ecological underpinnings of concern structures developed earlier in this book, and it is the order I use for this summary of normal accident theory.


Interactive complexity and coupling have ramifications for organizational governance and structuring. Both linear interaction and tight coupling require centralized management structures, whereas complex interaction and loose coupling require decentralized structures. Both interactive and management issues are described below.


P – Linear Interaction, Loose Coupling: Either Centralized or Decentralized Authority

There are few complex interactions in this system. Failed components can be isolated and worked around, without drastically disrupting system function. Accidents can be remedied in either a top-down manner from a central authority or a bottom-up manner from the floor. The prevalence of either form of management in linear, loosely coupled system will be more determined by organizational culture than by their systems and technologies. Single-goal agencies of all descriptions fit within this category, including government agencies. Most manufacturing operations and construction projects also share these qualities. These organizations exist to get specific tasks done, and the manner in which they get done does not need to be rigorously specified.


A – Linear Interaction, Tight Coupling: Centralized Authority

Regularized internal environment, predictable and visible interactions, and invariant sequences. Improvised workarounds are not possible, but must be explicitly design into the system. There is little slack in the system, and delays disrupt the entire operation. Bottom-up local or improvisational solutions may put the entire system at risk, so managerial authority is centralized. Projects in this category include hydroelectric dams, power distribution grids, continuous processing plants and refineries, and rail or marine transport. Centralization, unambiguous and explicit orders and policies and rigorous adherence to procedures are needed.


I – Complex Interaction, Tight Coupling: Neither Centralized nor Decentralized Authority

The tight coupling of the system makes any failure very disruptive, so local solutions have the potential to bring the whole system to a halt if they compromise functional integration with the larger systemic context. This is amplified by the complexity of the system, with components in close proximity to each other, heavily interconnected with many common-mode elements, vertical and horizontal dependencies and unexpected feedback loops. Many of the problems in such systems are unforeseeable because of the combinatorial complexity of the systems. Given this complexity, a decentralized approach to management is suggested, so that those closest to each subsystem can undertake a slow, careful search of the failure to determine what went wrong and what to do about it. However, this conflicts with the need to manage the tight coupling of overall system function. The only way this can be accommodated is for each unit to have a strong sense of the overall purpose of the system, as well as their own place in the system, and their responsibilities to other activity groups. That way they can be creative in the ways they make their needed contribution to overall system function.


E – Complex Interaction, Loose Coupling: Decentralized Authority

Complex interactions, with many control parameters and unplanned behaviors, require management by a network of operators each with some local expertise, particularly since troubleshooting will often be diagnostic and based on inference rather than straightforward observation. Furthermore, since the system is loosely coupled, there is some slack and some room to manoeuvre. Local ingenuity in finding substitutions and alternative pathways will not necessarily disrupt the whole system, and may improve it. Research and development organizations, universities and multi-goal agencies exhibit this kind of loose structure with distributed local authority. This permits the kind of local autonomy that encourages the development of innovations.


The greatest management challenge exists for tightly coupled complex systems with complex interactions, and these have the greatest normal accident potential as well. When a tightly coupled system has become complex, efforts must be made to reduce both coupling and complexity if possible. One way to accomplish this in management and technology is to use the same strategy used by human working memory – chunking. Tightly coupled elements can be integrated at a higher level of organization, through technology or the redefinition of certain activities. This chunking can make it quicker and easier for more people to exercise the coupled function. Perrow gives the example of air traffic control, and the development from early radio contact technologies to radar technologies and finally to transponders. This development took a multifaceted radio communications task and reduced it to an ‘at-a-glance’ representation of all needed information on a screen. By increasing the tight coupling of the linear interactions producing that information, the complexity of interaction managed by each individual operator went down. Also, by segregating traffic into types (commercial, military, small aircraft, etc) and assigning air corridors and altitudes by type, linearity was increased and the complexity of interaction decreased.


By reorganizing coupling, technologies release either operator time and attention, or restrictions on place of operation, or restrictions on the people who can operate that process. This can allow for a reassignment of roles. Within each new function, there may be tighter coupling and more linear interactions, but across the whole network there may be some loosening of coupling and encapsulation of function, pushing the system a bit closer towards a more manageable state. Object-oriented programming represents this kind of organizational development, relative to the procedural programming it has supplanted for certain tasks. To the degree to which programs must be complex, object-oriented programming loosens the coupling between encoded objects through encapsulation. To the degree to which programs must be tightly coupled, object-orientation shields the main program (as the higher level of the chunk) from some of the complexity of the overall code package (classes and objects on the lower level of the chunk). By chunking between levels of complexity and then integrating the resulting chunks, larger systems can be integrated in ways that manage the combined challenges of tight coupling and complexity.


This is central to the structure of concern:


P – In ecosystems, under r-selection conditions, loosely coupled, linear reactions produce the shortest energy-reduction pathways.


A – Under density conditions, larger, more centralized organizations with tighter coupling are more efficient at maximizing the reduction of resources that have become more scarce or patchy in time and space. However, there is an upper limit to the amount of complexity such a centralized system can manage. Fixes, workarounds, updates and expansions all increase the complexity of the system, until the single-system management strategy breaks apart.


I – A complex re-parcelling of the system is needed. Local autonomy must be balanced with global systemic integration. Local systems, organizing themselves to maximize their own reduction efficiency, also enhance the reductive capacity of the overall or global system by improving the efficiency of their input-output transactions with other nodes in the system.


E – When a community is in a climax condition, when further improvements in both independent and interdependent reduction efficiency provide diminishing returns, only an innovation can produce further appreciable enhancements. For this to happen there must be some loosening of coupling between system elements. Elements that can free themselves for some “evolutionary playtime” can produce this novelty. Novelty is often disruptive to the existing order, prompting the re-establishment of a new or altered overall system.


Organizational identity theory deals with two kinds of identifications. First there are the identities of the organizations as such, as expressed in public opinion about the organization and the way people relate to it as an entity. Then there are and the identities of people within those organizations, who identify themselves as part of the organization to some degree, and who on occasion speak for the organization.


In the first case, we must note that people represent organizations as social actors, and relate to them as such. In the second case, stakeholders within or around an organizations must build their own organizational identities that structure their interactions with other organizational members. These organizational identities combine work role, attitudes, values, degrees of centrality and commitment etc. for each organizational member.


Organizational identities are thus self-reflective. Members form their own interpretations of the organization’s identity in various ways. Those interpretations partially determine how members conduct themselves when they are acting ‘for’ the organization. That behavior partly determines the identity of the organization as a social agent, which in turn determines how other agents interact with ‘it’. Interpretations produce real effects through these feedback cycles (Rometsch, 2004).


So how do organizations perceive their own unity and distinctiveness, especially when there are likely to be a variety of different understandings of the organization among different group members over time?


Pratt and Foreman (2002) have developed a framework that lays out the options for dealing with multiple organizational identities along two intersecting dimensions: identity plurality and identity synergy. Plurality permits the expression of a variety of identities within a social grouping. This can be a very fruitful stance for a well-supported organization whose diversity is legitimized by stakeholders, like a neighbourhood supermarket where many of the customers know the employees by name. It can be inappropriate for organizations operating under tight resource constraints, such as a new in-town courier service trying to build a recognizable brand.


Synergy between or among organizational identities refers to tight interdependencies among the different identities, which must therefore be compatible. Low synergy responses indicate overly diverse identities that come into conflict with each other. Crossing these two dimensions gives us four styles of organizational identity. Ways of managing each one will differ.


P - Compartmentalization (high plurality, low synergy)

Identities are preserved with no attempt made to increase their interdependencies. This happens when the identities are legitimized by important stakeholders and they do not become diffused very much within the organization. Law firms, academic departments and other clusterings of self-directed professionals share this loose kind of organizational identification.


A - Deletion (low plurality, low synergy)

Managers consciously work to define normative identities and cultivate conformity, or to exclude identities or otherwise limit the number of organizational identities espoused. Deletion may be called for when stakeholders have withdrawn support for existing identities, when resources are constrained, or when existing identities are incompatible and achieving interdependence becomes too hard. When exercised extensively, deletion will produce one single hegemonic identity.


E - Aggregation (high plurality, high synergy)

Aggregation cultivates both variety and interdependence by forcing tighter links between diverse elements. The various elements have to be compatible, and stakeholders must generally approve of all of them. The pressure of aggregation can lead to the emergence of a meta-identity which reconciles potential contradictions among the identities in a dialectical fashion.


I - Integration (low plurality, high synergy)

Integration involves merging multiple individual organizational identities into a larger, distinctly new whole or collective identity. This is effective under the combined pressures of low stakeholder support for existing identities plus limited resources. Faced with the adversity, the time comes for the organization to "pull together".